Finite Group Databasebeta

← C5×#14513 #11937233

Subgroups — C5×#14513 #11937233

Order 1280.

1918 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#390C211yesmaximal, characteristic
2C2×C5×#386C211yesmaximal, characteristic
3C2×C5×#386C211yesmaximal, characteristic
4C5×#1442C212yesmaximal, complemented
5C5×#1439C212yesmaximal, complemented
6C5×#1439C212yesmaximal, complemented
7C5×#1436C212yesmaximal, complemented
8C5×C22⋊#95C212yesmaximal, complemented
9C5×C22⋊#95C212yesmaximal, complemented
10C23×C5×D4C2211yescharacteristic
11C24×C4×C5C2211yescharacteristic
12C24×C4×C5C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2212yes—
15C22×C5×C22⋊C4C2212yes—
16C22×C5×C22⋊C4C2212yes—
17C22×C5×C22⋊C4C2212yes—
18C22×C5×C22⋊C4C2211yescharacteristic
19C22×C5×C22⋊C4C2212yes—
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C42×C5C2211yescharacteristic
22C5×#390—24no—
23C5×#386—24no—
24C5×#386C418yescomplemented
25C2×C5×#95C2212yes—
26C2×C5×#95C2212yes—
27C2×C5×#95C2212yes—
28C2×C5×#95C2212yes—
29C2×C5×#95C2212yes—
30C2×C5×#95C2212yes—
31C2×C5×#95C2212yes—
32C2×C5×#95C2212yes—
33C2×C5×#95C2212yes—
34#14513C511yesmaximal, characteristic, direct product factor, Sylow
35C25×C5C2311yescharacteristic
36C25×C5C2311yescharacteristic
37C22×C5×D4—41no—
38C22×C5×D4—41no—
39C22×C5×D4—41no—
40C22×C5×D4—41no—
41C22×C5×D4C2×C414yes—
42C22×C5×D4D414yes—
43C22×C5×D4Q814yes—
44C23×C4×C5—22no—
45C23×C4×C5—24no—
46C23×C4×C5—42no—
47C23×C4×C5—42no—
48C23×C4×C5—42no—
49C23×C4×C5—41no—
50C23×C4×C5—41no—
51C23×C4×C5—41no—
52C23×C4×C5—41no—
53C23×C4×C5C2×C414yescomplemented
54C23×C4×C5C2312yes—
55C23×C4×C5C2312yes—
56C23×C4×C5C2312yes—
57C23×C4×C5C2312yes—
58C23×C4×C5C2312yes—
59C23×C4×C5C2312yes—
60C23×C4×C5C2311yescharacteristic
61C2×C5×C4⋊C4—22no—
62C2×C5×C4⋊C4—24no—
63C2×C5×C4⋊C4—41no—
64C2×C5×C4⋊C4—41no—
65C2×C5×C4⋊C4—42no—
66C2×C5×C4⋊C4—42no—
67C2×C5×C22⋊C4—24no—
68C2×C5×C22⋊C4—22no—
69C2×C5×C22⋊C4—24no—
70C2×C5×C22⋊C4—24no—
71C2×C5×C22⋊C4—24no—
72C2×C5×C22⋊C4—24no—
73C2×C5×C22⋊C4—24no—
74C2×C5×C22⋊C4—42no—
75C2×C5×C22⋊C4—42no—
76C2×C5×C22⋊C4—41no—
77C2×C5×C22⋊C4—41no—
78C2×C5×C22⋊C4—42no—
79C2×C5×C22⋊C4—42no—
80C2×C5×C22⋊C4—42no—
81C2×C5×C22⋊C4—41no—
82C2×C5×C22⋊C4—41no—
83C2×C5×C22⋊C4C2×C418yes—
84C2×C5×C22⋊C4C2×C414yescomplemented
85C2×C42×C5—22no—
86C2×C42×C5—41no—
87C2×C42×C5—41no—
88C5×#95—24no—
89C5×#95—24no—
90C5×#95—42no—
91C5×#95—42no—
92C5×#95—42no—
93C5×#95—42no—
94C5×#95—42no—
95C5×#95—42no—
96C5×#95C2×C418yescomplemented
97C2×#390C2×C511yescharacteristic
98C2×#386C2×C511yescharacteristic
99C2×#386C2×C511yescharacteristic
100#1442C2×C512yescomplemented
101#1439C2×C512yescomplemented
102#1439C2×C512yescomplemented
103#1436C2×C512yescomplemented
104C22⋊#95C2×C512yescomplemented
105C22⋊#95C2×C512yescomplemented
106C24×C5—22no—
107C24×C5—22no—
108C24×C5—22no—
109C24×C5—22no—
110C24×C5—22no—
111C24×C5—22no—
112C24×C5—22no—
113C24×C5—22no—
114C24×C5—21no—
115C24×C5—21no—
116C24×C5—21no—
117C24×C5—21no—
118C24×C5—21no—
119C24×C5—21no—
120C24×C5—21no—
121C24×C5—21no—
122C24×C5C22×C412yes—
123C24×C5C22×C412yes—
124C24×C5C2×D412yes—
125C24×C5C2×D412yes—
126C24×C5C2×Q812yes—
127C24×C5C2×Q812yes—
128C24×C5C2411yescharacteristic
129C2×C5×D4—44no—
130C2×C5×D4—44no—
131C2×C5×D4—44no—
132C2×C5×D4—44no—
133C2×C5×D4—44no—
134C2×C5×D4—44no—
135C2×C5×D4C4⋊C4116yescomplemented
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5—22no—
154C22×C4×C5—22no—
155C22×C4×C5—22no—
156C22×C4×C5—22no—
157C22×C4×C5—22no—
158C22×C4×C5—22no—
159C22×C4×C5—22no—
160C22×C4×C5—22no—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5—22no—
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5—22no—
167C22×C4×C5—22no—
168C22×C4×C5—22no—
169C22×C4×C5—22no—
170C22×C4×C5—22no—
171C22×C4×C5—22no—
172C22×C4×C5—22no—
173C22×C4×C5—22no—
174C22×C4×C5—22no—
175C22×C4×C5—22no—
176C22×C4×C5—22no—
177C22×C4×C5—22no—
178C22×C4×C5—48no—
179C22×C4×C5—44no—
180C22×C4×C5—44no—
181C22×C4×C5—48no—
182C22×C4×C5—48no—
183C22×C4×C5—44no—
184C22×C4×C5—48no—
185C22×C4×C5—44no—
186C22×C4×C5—44no—
187C22×C4×C5—44no—
188C22×C4×C5C22×C414yes—
189C22×C4×C5C22×C414yes—
190C22×C4×C5C22×C412yes—
191C22×C4×C5C2×D412yes—
192C22×C4×C5C2×Q812yes—
193C22×C4×C5#4114yes—
194C22×C4×C5#4114yes—
195C5×C4⋊C4—44no—
196C5×C4⋊C4—48no—
197C5×C22⋊C4—48no—
198C5×C22⋊C4—44no—
199C5×C22⋊C4—48no—
200C5×C22⋊C4—48no—
201C5×C22⋊C4—48no—
202C5×C22⋊C4—44no—
203C42×C5—44no—
204C23×D4C22×C511yescharacteristic
205C24×C4C22×C511yescharacteristic
206C24×C4C22×C511yescharacteristic
207C22×C4⋊C4C22×C512yes—
208C22×C4⋊C4C22×C511yescharacteristic
209C22×C22⋊C4C22×C512yes—
210C22×C22⋊C4C22×C512yes—
211C22×C22⋊C4C22×C512yes—
212C22×C22⋊C4C22×C511yescharacteristic
213C22×C22⋊C4C22×C512yes—
214C22×C22⋊C4C22×C511yescharacteristic
215C22×C42C22×C511yescharacteristic
216#390—24no—
217#386—24no—
218#386C4×C518yescomplemented
219C2×#95C22×C512yes—
220C2×#95C22×C512yes—
221C2×#95C22×C512yes—
222C2×#95C22×C512yes—
223C2×#95C22×C512yes—
224C2×#95C22×C512yes—
225C2×#95C22×C512yes—
226C2×#95C22×C512yes—
227C2×#95C22×C512yes—
228C23×C5—24no—
229C23×C5—24no—
230C23×C5—22no—
231C23×C5—24no—
232C23×C5—22no—
233C23×C5—24no—
234C23×C5—22no—
235C23×C5—22no—
236C23×C5—22no—
237C23×C5—22no—
238C23×C5—22no—
239C23×C5—22no—
240C23×C5—22no—
241C23×C5—22no—
242C23×C5—22no—
243C23×C5—22no—
244C23×C5—24no—
245C23×C5—24no—
246C23×C5—24no—
247C23×C5—24no—
248C23×C5—24no—
249C23×C5—24no—
250C23×C5—24no—
251C23×C5—24no—
252C23×C5—42no—
253C23×C5—42no—
254C23×C5—42no—
255C23×C5—42no—
256C23×C5—42no—
257C23×C5—42no—
258C23×C5—42no—
259C23×C5—42no—
260C23×C5—41no—
261C23×C5—41no—
262C23×C5—42no—
263C23×C5—42no—
264C23×C5—41no—
265C23×C5—41no—
266C23×C5—42no—
267C23×C5—41no—
268C23×C5—42no—
269C23×C5—41no—
270C23×C5—41no—
271C23×C5—41no—
272C23×C5C2×C4⋊C414yes—
273C23×C5C2×C4⋊C414yes—
274C23×C5C23×C411yescharacteristic
275C23×C5C22×D411yescharacteristic
276C23×C5C22×Q811yescharacteristic
277C23×C5C2×#4112yes—
278C23×C5C2×#4112yes—
279C23×C5H(5,𝔽2)11yescharacteristic
280C23×C5H(5,𝔽2)11yescharacteristic
281C23×C5H(5,𝔽2)11yescharacteristic
282C23×C5H(5,𝔽2)11yescharacteristic
283C23×C5H(5,𝔽2)12yes—
284C23×C5H(5,𝔽2)12yes—
285C5×D4—416no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5—22no—
292C2×C4×C5—24no—
293C2×C4×C5—24no—
294C2×C4×C5—24no—
295C2×C4×C5—24no—
296C2×C4×C5—24no—
297C2×C4×C5—24no—
298C2×C4×C5—24no—
299C2×C4×C5—24no—
300C2×C4×C5—24no—
301C2×C4×C5—24no—
302C2×C4×C5—24no—
303C2×C4×C5—24no—
304C2×C4×C5—416no—
305C2×C4×C5—416no—
306C2×C4×C5—42no—
307C2×C4×C5—42no—
308C2×C4×C5—42no—
309C2×C4×C5—42no—
310C2×C4×C5—42no—
311C2×C4×C5—42no—
312C2×C4×C5—42no—
313C2×C4×C5—42no—
314C2×C4×C5—42no—
315C2×C4×C5—42no—
316C2×C4×C5—42no—
317C2×C4×C5—42no—
318C2×C4×C5—42no—
319C2×C4×C5—42no—
320C2×C4×C5—42no—
321C2×C4×C5—42no—
322C2×C4×C5—42no—
323C2×C4×C5—42no—
324C2×C4×C5—42no—
325C2×C4×C5—42no—
326C2×C4×C5—42no—
327C2×C4×C5—42no—
328C2×C4×C5—42no—
329C2×C4×C5—42no—
330C2×C4×C5—42no—
331C2×C4×C5—42no—
332C2×C4×C5—42no—
333C2×C4×C5—42no—
334C2×C4×C5—42no—
335C2×C4×C5—42no—
336C2×C4×C5C2×C4⋊C414yes—
337C25C23×C511yescharacteristic
338C25C23×C511yescharacteristic
339C22×D4—41no—
340C22×D4—41no—
341C22×D4—41no—
342C22×D4—41no—
343C22×D4C2×C4×C514yes—
344C22×D4C5×D414yes—
345C22×D4C5×Q814yes—
346C23×C4—22no—
347C23×C4—24no—
348C23×C4—41no—
349C23×C4—41no—
350C23×C4—41no—
351C23×C4—41no—
352C23×C4—42no—
353C23×C4—42no—
354C23×C4—42no—
355C23×C4C2×C4×C514yescomplemented
356C23×C4C23×C512yes—
357C23×C4C23×C512yes—
358C23×C4C23×C512yes—
359C23×C4C23×C512yes—
360C23×C4C23×C512yes—
361C23×C4C23×C512yes—
362C23×C4C23×C511yescharacteristic
363C2×C4⋊C4—22no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4—41no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4—41no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—41no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4C2×C4×C518yes—
386C2×C22⋊C4C2×C4×C514yescomplemented
387C2×C42—22no—
388C2×C42—41no—
389C2×C42—41no—
390#95—24no—
391#95—24no—
392#95—42no—
393#95—42no—
394#95—42no—
395#95—42no—
396#95—42no—
397#95—42no—
398#95C2×C4×C518yescomplemented
399C22×C5—24no—
400C22×C5—24no—
401C22×C5—28no—
402C22×C5—28no—
403C22×C5—44no—
404C22×C5—44no—
405C22×C5—42no—
406C22×C5—42no—
407C22×C5—42no—
408C22×C5—42no—
409C22×C5—42no—
410C22×C5—42no—
411C22×C5—44no—
412C22×C5—44no—
413C22×C5—42no—
414C22×C5—42no—
415C22×C5—42no—
416C22×C5—42no—
417C22×C5—44no—
418C22×C5—44no—
419C22×C5—42no—
420C22×C5—42no—
421C22×C5C22×C4⋊C411yescharacteristic
422C22×C5C4×#4112yes—
423C22×C5#51811yescharacteristic
424C22×C5#51811yescharacteristic
425C22×C5#51812yes—
426C22×C5#53411yescharacteristic
427C22×C5#53411yescharacteristic
428C22×C5#53812yes—
429C22×C5#53812yes—
430C22×C5#54012yes—
431C22×C5#54012yes—
432C22×C5#54311yescharacteristic
433C22×C5#54311yescharacteristic
434C22×C5#54612yes—
435C22×C5#54612yes—
436C22×C5#55111yescharacteristic
437C22×C5#55312yes—
438C22×C5#55412yes—
439C22×C5#55412yes—
440C22×C5#55911yescharacteristic
441C22×C5#56012yes—
442C22×C5#56011yescharacteristic
443C22×C5H(3,𝔽4)11yescharacteristic
444C4×C5—24no—
445C4×C5—44no—
446C4×C5—44no—
447C4×C5—44no—
448C4×C5—44no—
449C4×C5—82no—
450C4×C5—82no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24C22×C4×C512yes—
468C24C22×C4×C512yes—
469C24C2×C5×D412yes—
470C24C2×C5×D412yes—
471C24C2×C5×Q812yes—
472C24C2×C5×Q812yes—
473C24C24×C511yescharacteristic
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4C5×C4⋊C4116yescomplemented
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—48no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—48no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4C22×C4×C514yes—
534C22×C4C22×C4×C514yes—
535C22×C4C22×C4×C512yes—
536C22×C4C2×C5×D412yes—
537C22×C4C2×C5×Q812yes—
538C22×C4C5×#4114yes—
539C22×C4C5×#4114yes—
540C4⋊C4—44no—
541C4⋊C4—48no—
542C22⋊C4—48no—
543C22⋊C4—44no—
544C22⋊C4—48no—
545C22⋊C4—48no—
546C22⋊C4—48no—
547C22⋊C4—44no—
548C42—44no—
549C2×C5—44no—
550C2×C5—44no—
551C2×C5#231511yescharacteristic
552C2×C5#233312yes—
553C2×C5#234912yes—
554C2×C5#237411yescharacteristic
555C2×C5#237511yescharacteristic
556C2×C5#268411yescharacteristic
557C2×C5#268812yes—
558C2×C5#270911yescharacteristic
559C2×C5#274811yescharacteristic
560C2×C5#278012yes—
561C2×C5#280411yescharacteristic
562C23—24no—
563C23—24no—
564C23—22no—
565C23—24no—
566C23—22no—
567C23—24no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—41no—
595C23—41no—
596C23—42no—
597C23—42no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—42no—
602C23—41no—
603C23—42no—
604C23—41no—
605C23—41no—
606C23C2×C5×C4⋊C414yes—
607C23C2×C5×C4⋊C414yes—
608C23C23×C4×C511yescharacteristic
609C23C22×C5×D411yescharacteristic
610C23C22×C5×Q811yescharacteristic
611C23C2×C5×#4112yes—
612C23C2×C5×#4112yes—
613C23C5×H(5,𝔽2)11yescharacteristic
614C23C5×H(5,𝔽2)11yescharacteristic
615C23C5×H(5,𝔽2)11yescharacteristic
616C23C5×H(5,𝔽2)11yescharacteristic
617C23C5×H(5,𝔽2)12yes—
618C23C5×H(5,𝔽2)12yes—
619D4—416no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—416no—
639C2×C4—416no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4C2×C5×C4⋊C414yes—
671C5#1451311yescharacteristic, direct product factor, Sylow
672C22—24no—
673C22—24no—
674C22—28no—
675C22—28no—
676C22—42no—
677C22—42no—
678C22—44no—
679C22—44no—
680C22—42no—
681C22—42no—
682C22—44no—
683C22—44no—
684C22—42no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22—44no—
691C22—44no—
692C22—42no—
693C22—42no—
694C22C22×C5×C4⋊C411yescharacteristic
695C22C4×C5×#4112yes—
696C22C5×#51811yescharacteristic
697C22C5×#51811yescharacteristic
698C22C5×#51812yes—
699C22C5×#53411yescharacteristic
700C22C5×#53411yescharacteristic
701C22C5×#53812yes—
702C22C5×#53812yes—
703C22C5×#54012yes—
704C22C5×#54012yes—
705C22C5×#54311yescharacteristic
706C22C5×#54311yescharacteristic
707C22C5×#54612yes—
708C22C5×#54612yes—
709C22C5×#55111yescharacteristic
710C22C5×#55312yes—
711C22C5×#55412yes—
712C22C5×#55412yes—
713C22C5×#55911yescharacteristic
714C22C5×#56011yescharacteristic
715C22C5×#56012yes—
716C22C5×H(3,𝔽4)11yescharacteristic
717C4—24no—
718C4—44no—
719C4—44no—
720C4—44no—
721C4—44no—
722C4—82no—
723C4—82no—
724C2—44no—
725C2—44no—
726C2C5×#231511yescharacteristic
727C2C5×#233312yes—
728C2C5×#234912yes—
729C2C5×#237411yescharacteristic
730C2C5×#237511yescharacteristic
731C2C5×#268411yescharacteristic
732C2C5×#268812yes—
733C2C5×#270911yescharacteristic
734C2C5×#274811yescharacteristic
735C2C5×#278012yes—
736C2C5×#280411yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC23×C5×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C5×#1442C2semidirect
5. C5×#1439C2semidirect
6. C5×#1439C2semidirect
7. C5×#1436C2semidirect
8. C5×C22⋊#95C2semidirect
9. C5×C22⋊#95C2semidirect
24. C5×#386C4semidirect
34. #14513C5direct (N × H)
53. C23×C4×C5C2×C4semidirect
84. C2×C5×C22⋊C4C2×C4semidirect
96. C5×#95C2×C4semidirect
100. #1442C2×C5semidirect
101. #1439C2×C5semidirect
102. #1439C2×C5semidirect
103. #1436C2×C5semidirect
104. C22⋊#95C2×C5semidirect
105. C22⋊#95C2×C5semidirect
135. C2×C5×D4C4⋊C4semidirect
218. #386C4×C5semidirect
355. C23×C4C2×C4×C5semidirect
386. C2×C22⋊C4C2×C4×C5semidirect
398. #95C2×C4×C5semidirect
480. C2×D4C5×C4⋊C4semidirect
671. C5#14513direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C5×#3902
C2×C5×#3862
C5×#14422
C5×#14392
C5×#14362
C5×C22⋊#952
#145135